[3 level meta analysis] is tau^2= zero possible?

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James Lee's picture
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Joined: 06/17/2013

My clustered several variables into a model. this set below is one of them
Overall, 6 clusters including the data set below are created.

I chose 3 level meta analysis cause level 3 is proven to be preffered according to anova() comparison.
However, Tau2_2 in the data is extremely low almost 0 with 3 decimal. this is the same for all other clusters.
and the overall model.

My question is that is there any constraint that works? or is it possible outcome?

Call:
meta3(y = fisherz, v = v, cluster = id, x = cbind("dis", "review"),
data = KORdb, intercept.constraints = 0, model.name = "Modelpub")

95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Slope_1 3.0175e-01 3.1594e+02 -6.1892e+02 6.1953e+02 0.0010 0.99924
Slope_2 3.0175e-01 3.1594e+02 -6.1892e+02 6.1953e+02 0.0010 0.99924
Tau2_2 9.9365e-11 1.0092e-02 -1.9779e-02 1.9779e-02 0.0000 1.00000
Tau2_3 3.9636e-02 1.5767e-02 8.7337e-03 7.0537e-02 2.5139 0.01194 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Mike Cheung's picture
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Joined: 10/08/2009
Dear James, I have a couple

Dear James,

I have a couple of comments.
1. Since the sample data and the syntax were not attached, I cannot tell whether there are something wrong in the package, in the data or in the syntax.
2. The estimated values for Tau2_2 and Tau2_3 can be 0 or even negative for small number of groups. meta3() sets the lower bound of Tau2_2 and Tau2_3 to 1e-10. You may change this default. See the arguments RE2.lbound and RE3.lbound in the help manual of meta3.
3. Since you have imposed intercept.constraints = 0, I assume that "dis" and "review" are the two dummy variables for one variable. If "dis" and "review" represent two variables, intercept.constraints = 0 should not be imposed. See http://courses.nus.edu.sg/course/psycwlm/Internet/metaSEM/3level.html#se... for an example

Mike

James Lee's picture
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Joined: 06/17/2013
What initial value do i need to set if tau2_2 is 1e_10?

Always thanks a lot.

In your second comment, "dis" and "review" are dummy. So I guess small number of groups cause this
consequence. As you mentioned, Tau2_2 was 1e_10 which was almost "zero".

You suggest that i can change this initial value into another one with Re2 or Re3.lbound command.
But, I have a question. What initial value do I have to set, instead?

Regards

Mike Cheung's picture
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Joined: 10/08/2009
The lower bounds are set to

The lower bounds are set to ensure that the estimates of the variances are non-negative. 1e-10 should be small enough. I am not suggesting that you should change it to other values.

Mike